Disclaimer, as requested by Digital Instruments: Nanoscope
is a registered trademark of Digital Instruments, Inc., and TappingMode,
AutoTune, and are tradmarks of Digital Instruments. Although this
manual is for DI products, DI is not responsible for its content, so if
you break your AFM using one of these procedures, its not their fault,
(and for that matter it's not the Colvin Group's either). Questions about
this disclaimer may be forwarded to Bobbie Offen, BobbieO@di.com.

Note: Our group uses Digital Instruments TESP
tips (fo between 200 and 350 KHz). If you
do not use TESP's, the procedure for optimizing your TM-AFM may very slightly,
and the value of parameters that you should use will also vary.

I. Introduction:

Tapping ModeTM Atomic Force Microscopy (TM-AFM) works by
vibrating a tip which is at the end of a cantilever and bringing the tip
into intermittent contact with a sample surface. When the tip interacts
with a surface feature, its amplitude is decreased from its previous amplitude
of oscillation. The AFM senses this decrease, and the tip is raised away
from the sample in order to re-attain the previous amplitude of oscillation.
In this way, the tip can be rastered across the sample to generate topographical
images. Because the reaction of the tip is sensitive to sample mechanical
properties, such as viscoelasticity, we can also gain an understanding
of these quantities through TM-AFM.

TM-AFM has a number of advantages over other microscopic techniques.
One is the ability to image soft samples without damaging them, and for
this reason TM-AFM is very useful for imaging biological and polymer samples.
It also has the advantage of being fairly easy to use and requires little
sample preparation.. The resolution of TM-AFM is arguable though it is
certainly less than contact mode AFM. It is probably about 5 nm..

II. TM-AFM Theory

In order to understand TM-AFM, it is necessary to understand oscillators.
We will therefore first do a little review.

A. Review of Harmonic Oscillators

The most simple expression for springs is Hooke's Law.

By Newton's Second Law, this is equal to

As is usual with physics, this is a gross oversimplification of anything
we would encounter in real life. There are two additional forces besides
the tension in the spring which effect the motion of most oscillators one
encounters, including the AFM cantilever. These forces are damping and
driving.

Damping is a frictional force, and like the friction of a piece of wood
being pushed across a floor, the damping force is proportional to the negative
of the velocity (i.e., it opposes the motion). Thus,

The expression for the driving force depends (oddly enough) on how you
drive it. Since it is generally nice for oscillators to oscillate, a typical
driving force is

Thus the driving force has some maximum amplitude Fo and
a frequency omega (not to be confused with omegao, the resonance
frequency of the free, undamped oscillator).Summing the forces, we get
the equation for damped, driven oscillators.

Most textbooks or articles are not content to leave the equation in
this form, however. A common term which is substituted is Q, the quality
factor of the spring. Q is defined as

Where omegaR is the resonance frequency of the damped driven
oscillator,

and Beta = b/2m. If you do a lot of algebra, you can find that

Usually we can ignore the ½, (Q >> 1) so we get

Thus, we can substitute the above into Eq. 5 for b, and obtain another
form of the equation of motion

It is also common for textbooks to divide this equation through by m,
then using the definition of undamped resonance frequency,

obtaining

B. Modeling the AFM Cantilever

Since the cantilever is essentially, as Science (v.207, p.1983)
calls it, "a wee diving board", i.e., a driven damped oscillator, J. Tomayo
and R. Garcia (Langmuir, v.12, pp.4430 - 4435) had the neat idea
of modeling it using Eq.6. However, now one must consider another
force, that of the surface.

If the system is set-up as in Figure 1, then the differential equation
of motion is:

which is just Eq. 6 with an F(zc,z) term inserted to account
for the surface interactions. This term depends on whether or not the tip
in contact with the surface (i.e., zc+z > ao) or
not (zc+ z <= ao)

where parameters are defined in Table 1.

When the tip is not in contact, the only force it feels from the sample
is van der Waals, which is attractive. When in contact, there is
the attractive van der Waals force over the interatomic distances, and
the repulsive force due to sample hardness (the Young's modulus term).
The third term is due to viscosity and acts like a friction force, opposing
the motion of the tip. While the terms involving Young's modulus
and viscosity make the model more difficult, if we model the system correctly,
we can obtain these two sample parameters that cannot be obtained by other
microscopic techniques.

C. Lessons to be Learned from the Model

The most important thing to get from theoretical modeling is that the
tip does not simply push itself into a surface it comes in contact with.Such
behavior would not be consistent with the differential equations. Instead,
it decreases its amplitude of oscillation in a nearly linear manner, which
allows it to continue to satisfy the equations.

III. Getting Started in TM-AFM

A. Turning the Instrument On

The power switch is on the back right of the main computer. Also turn
on the optical microscope lamp (Cream colored box with black switch to
back right of microscope) and the monitor for the video camera (switch
on front). The video camera is usually on. You will know you turned on
the machine because you'll see numbers appear on the AFM.

B. Loading a Tip in the Microscope

1) Prepare a sophisticated tip holder. Use a 5 inch piece of
copper wire. Cut a small piece of double sticky tape and press one end
of the Cu wire down against the tape -- it should stick to the wire.

2) Move the actual AFM tip off of the storage cases' sticky tape.
The
AFM tips come packaged in plastic containers with a sticky tape area used
for stabilizing the tips. Using a pair of tweezers move one of these tips
off the sticky tape area.

3) Place the tip under the tab on the tip holder piece. Using
your special copper wire device from (1), touch the tip just to
the right of the line running vertically to the long axis. Don't put it
too far to the right or you will hurt the AFM tip. Too far to the left
and you'll block the electronics. Lift the tip up into the air. With the
tip holder assembly upside down, press down on it -- this will cause a
small tab of metal to come up and you can then slide the left part of the
AFM tip in. Stop pressing on the tip holder and the metal tab should be
securing the tip in place.

4) Readjust slightly the tip position if it is really crooked. It
doesn't matter too much that the tip be set at a perfect right angle to
the tip holder; however, you can set it in well and ensure electrical contact
by using a pair of tweezers to rotate the tip slightly to align it coarsely.
If you need to adjust the position of the tip in the holder, you can push
the tip around by inserting the tweezer tip into the intersection of the
grooves on the tip.

C. Loading a Sample into
the Microscope.

1) Put sample on holder and slide stage into microscope. The
sample holder is a circular metallic disk which is magnetic and sticks
to the magnetic stage. Use double sticky tape to hold down the sample to
the puck. Place a piece of mica on top of this and use scotch tape
to take off the first layer. You can then apply your sample. The sample/puck
assembly can be easily placed in the AFM using a pair of tweezers.

2) Put the Tip Holder Assembly Into the Microscope. Use the "Tip
Up" toggle switch to bring the tip away from the sample. If
you do not do this you risk breaking your tip. Flip the tip holder
over so the metal rod is out and the copper tabs face up and the tip down.
Slide the tip holder into the microscope and let it gently come to rest
on the two ball points in the scanner head. Watch through the optical
microscope as you twist the large knob (See Figure 4) directly behind the
sample stage to lower the electrical connectors down onto the tip holder.
If the tip looks shiny STOP! The tip
has come in contact with the sample. Do a tip up immediately, and you may
salvage the tip.

D. Aligning the Tip for Operation

1) Get the optical microscope working. First make sure that you
have light on the system (turn on the black knob #1 in Figure 2). Next,
look through the eyepiece- you should see light. If not, then move shutter3
to put the view to the eyepiece. It may not look in focus. You should generally
be able to focus on the sample area using the focus knob (#4). If you have
trouble bringing anything into focus it may be that the optical microscope
is lifted up and away from the AFM. Lower the whole microscope by turning
the largest black knob in the back right- make sure you support the microscope,
and never turn the two black knobs on either side of the microscope.
If the optical microscope falls it could crush the very expensive AFM and
you will have your salary garnished for the rest of your life.

2) Centering Tip and Sample in Field of View. Using the lower
knobs (See Figure 1) on the stage that supports the whole AFM, bring the
tip and sample into view (See Figure 3). You can use the eyepiece first
to grossly get the tip into the center, then switch to the video screen
using the shutter (#3 in Figure 2).

3) Get tip close to surface. You want to bring the tip close
enough to the surface that your alignment procedures work well, but not
to close as to crash it into the surface. Begin by using the focus knob
to focus on the sample surface. Go past (or "up") the sample focus to comeback
to your tip. Then reverse from this position -- you should bring the sample
surface back into focus again, then go past this focus to bring the back
reflection of the tip into focus. Then move back to the sample focus. This
exercise is important, because you'll know that you are indeed looking
at the sample surface, not its virtual image. Now, use the black
lever (Figure 4) to push the tip down until it gets into better focus.DON'T
BRING THE TIP INTO COMPLETE FOCUS(this will crash it)- instead
just make its shape distinct.

4) Get laser on tip. Turn down the microscope light using knob#1
on the cream box. On the video you should see a wash of red light which
is the laser. Using the 2 laser positioning knobs (X and Y in Figure 4),move
the laser so that it is centered on the tip (see Figure 3).

5) Alignment- fine adjust in intensity. Look at the bar that
wraps around the large oval circle on the bottom of the microscope. Adjust
the mirror position using the lever (#1 in Fig. 4) in the back of the microscope
to maximize the bar. For a TESP tip the bar reading should be between 2
and 3 after alignment.

7) Photo-diode adjustment. Now you want to get the light centered
on the position sensitive detector. Your goal is to make the number in
the oval equal to zero (+/- 1 is OK). You will be moving the two knobs
(A and B in Figure 4) which control the position of the detector while
watching the number in the oval. Using A, turn the knob counter-clockwise
to make it decrease, or clockwise to make it increase. Usually this
should do it. However, if you notice the bar graph decreasing, turn
A back to where it was and use B.

8) Isolation Platform and the Seuss Hat. At some point, you may
need extra vibrational and acoustical isolation of the AFM from the surroundings.
In this case, you can use the isolation table, which is just a piece of
granite suspended from a tripod by bungee cords, and the Seuss hat, a felt
cylindrical cover. Vewy vewy cewfuwy move the very very expensive
AFM over to the isolation table. Make sure that the cord that looks
like a SCSI cord does not catch on the base of the adjustment table (Todd
Day at DI has asked me to note that the cord is not a SCSI, so please
don't try to hook it up to anything like a zip drive as the 440V that the
cord carries will fry it instantaneously). Place the Seuss hat over the
AFM. Note: you need not do this for standard imaging conditions,just
when things are really noisy or you are trying to see something very small.
Make sure you have a working tip before you do this, because it is a pain
to have to move it back to the table and realign or replace the tip.

IV. Data Acquisition

A. Description of Data Types

There are two types of data that are commonly used, height and phase.
Other data types are available, such as deflection, but are not included
here.

1) Height Data. Height data, or topography, is often the most
useful and reliable data that can be obtained from the AFM. In TM-AFM,
when the cantilever encounters a surface feature, its amplitude of oscillation
is decreased from its set-point value (Fig. 6, top). This decrease is noted
by the sensor and the tip is moved up away from the sample to re-attain
the set-point amplitude (Fig. 6, middle). When the tip moves past the feature,
its amplitude will increase, and the tip will be moved down again so that
the amplitude is once again brought back to the set-point (Fig. 6, bottom).

2) Phase Data. Phase data is obtained from the difference between
the driven and the actual oscillations of the cantilever.

Figure 7 (DI publication "Phase Imaging: Beyond Topography") illustrates
how phase data is obtained. The tip is driven with Focos(wt-
phid), but the actual response of the tip is Focos(wt
- phir). The phase offset caused by interaction with the surface
is then phid - phir. Phase is useful because different
materials will cause different offsets in phase, due to the fact that it
depends on differences in adhesion, friction and viscoelasticity. In Fig.
7, Sample 1 has a much smaller phase offset than Sample 2, so they will
be very distinguishable in phase imaging. Phase images will also display
great sensitivity to fine ridges in materials, often helping the user to
locate areas of interest.

B. Basics of Data Acquisition

1) Start the program: Hit "Z" to start from Windows 95

2) Tune the tip. Hit the little tuning fork icon. Because other
users will utilize different scan parameters than you, you should hit the
"Manual" button to see that the parameters are acceptable for use with
TESP tips. Typical settings are listed in Table 2.

Table 2. Quick Reference for Scan Parameters*

Parameter

Definition

Typical Value

Range of Values

Effect on Image Quality

Setpoint

The value of the RMS of the
cantilever vibration amplitude that the feedback loop maintains. (Setpoint
is thus proportional to force applied to surface)

2.00 V

1.00 V - 5.00 V

Reducing setpoint often leads to better quality images

Drive Amplitude

The amplitude of the force at which the cantilever is driven (Foin
Eq. 6)

50 mV

30 mV - 1.00 V

Increasing drive amplitude often gives better phase data, up to a point

Proportional and Integral Gains

Determine how sensitive the feedback loop is to variations in the tip's
amplitude of oscillation

0.400/4.00

0-0.600/0-6.00

Increasing gains often helps obtain better images (especially height)but
only up to a point, above which high
frequency noise is observed

Scan Rate

Controls the rate at which the cantilever scans across the sample area

2.00 Hz

1.00 Hz - 4.00 Hz

A slower scan rate generally leads to better images, but not always.
Decease until you get the best image

Number of Samples

The number of pixels used to create the image

256

128-512

Increasing leads to better image quality, but there is a trade-off
with time

3) Approach the Surface. Hit the down green arrow icon, which
will cause the tip to approach the surface of the sample. You can monitor
the progress of the tip engagement by watching the bottom of the control
screen.

C. Optimization of Scan Parameters

Do not try to optimize the image by observing the image! Instead,
hit the "Scope mode" icon (looks like an oscilloscope). You'll see a graph
of z-position versus xy positions. The white and yellow lines represent
the trace and retrace of the tip as it is rastered across the sample. Since
the difference in space between the trace and retrace is small, these two
should closely agree, so the white and yellow lines should overlap. If
the white and yellow lines do not overlap, follow this procedure:

1) Decrease the Set Point. Do this until the image improves or
until you reach 1.0 V

2) Increase the Drive Amplitude. Often times there will be a
significant amount of strong noise. Increasing the Drive Amplitude will
take care of this. Once you have a good picture, back off on Drive Amplitude
as much as you can without coming off the surface. The following set of
images is ordered by drive amplitude, from lowest to highest (60 to 200mV).

As you can see, the best quality images are at the lower drive amplitudes.

3) Change the gains. High values of gain may cause high frequency
noise, so it is often necessary to reduce their value, keeping them in
approximately a 1:10 integral to proportional ratio. However, the gains
should be kept as high as possible, since they control how fast the cantilever
will respond to changes in topography.

4) Change the scan rate. If reducing the gains does not eliminate
noise, this can help. Scan rate values that are too low as well as too
high will cause poor images. You should try a range of values while in
image mode to obtain the best one.

5) Adjust the Z Range. Although this can be changed later (e.g.,
in Flatten), it is often important to have the most contrast available
while in you are imaging. Thus, you should set the Z Range in such a way
that the scope mode picture just fits within the Z Range.

D. Data Analysis and Output

1) Capturing data. In order to save your image files and to be
able to do data analysis, you must first capture the image. First go to
the Capture menu, and select "Capture Filename". Name the file something
that makes sense to you, but try to keep it systematic (e.g., your initials,
a date and another letter) as you will eventually take large numbers of
images. Once you have done this, you can capture any picture by clicking
the camera icon. You can monitor the status of your capture by looking
at the bottom of the control screen. If you are in the middle of an image,
it will probably give you the message, "Capture: Next". In this case, hit
either the arrow up or arrow down icon, which will start your scan from
the bottom or the top. Be sure that while you are trying to capture an
image you do not adjust the scan parameters. Doing so will reset the capture
to take the next image. When the capture is complete, it will say "Capture:
Done".

2) Data Analysis. Once you have captured an image, you can analyze
it with the many tools supplied by the DI software. First, click on the
TV screen at the left of the control screen. Now go to the "Image" menu,
and select right or left image. Full details of data convolution and analysis
will be included in the next version of this manual. For now, let it be
said that it is generally necessary to "Flatten" the image before it can
be used. This is done by hitting the rolling pin icon.

A very useful data analysis tool is "Section". Select this from the
"Analysis" menu. By clicking on the image and drawing a line between points,
you can see a plot of Z versus the axis you have drawn. This is handy in
determining the size (width) of nanoparticles, for example.

3) Output. You now probably want to get your data off the machine
so you can show your family and friends. To simply get an image, go to
the "Utility" menu and select "Tiff Export". This will give you a dialogue
box. It is important that you choose "Reverse" under background, because
if you print these out, you do not want a lot of black surrounding your
image - that will significantly slow down your printing time. Select a
filename somewhere on the C:\ drive.

If you want to get another picture, e.g., a section analysis, you must
choose "Print" from the dialogue box and set destination to "TIFF".

To copy your files to a portable disk (floppy, zip, etc.) you must exit
the AFM program and return to Windows. If you need to zip up your files,
you can use the DOS version of pkzip which is installed on the CNST's AFM.

V. Helpful Hints and Trouble-shooting

A. Protecting Your Investment,
or, Stupid Ways to Break Tips

The biggest cost involved in day-to-day AFM-ing is for cantilever tips.
A box of 10 TESP tips from Digital Instruments runs $400. Thus, it is important
to be careful and not break these precious commodities. Here is a list
of things to avoid doing while handling the tips.

Avoid touching the tips anywhere near the cantilever end, especially with
the copper wire with tape at the end

When you pull the tips off the sticky tape in the box using the tweezers,
do not bend them forward in the direction of the tip

Do not drop the tip on any surface. This includes, but is not limited to,
the desk, the floor, and your lap

When you place the tip holder in the AFM, hold it well above the sample
so as not to scrape the tip across the sample

When you place the tip holder in the AFM, be sure that you do a tip up(i.e.,
sample down) first to make sure that you will not hit the sample

B. Trouble-Shooting

Here are a few problems you may encounter in the course of doing AFM.

1) AutoTuneTM will not work.

Make sure that the tip holder has been secured in the AFM and you have
turned the knob to enable electrical contact (Sec III.C.3).

Make sure that your tip is not in contact with the sample. You will know
that it is in contact if the tip looks shiny through the optical microscope.
If so, do a tip up, and the tip may still be OK.

2) Sample seems to move when lowering the tip.

This probably means that you have placed the sample in such a way that
it is coming in contact with the tip holder. Rotate the sample so that
any part of it that is hanging over the piezo-tube are coming towards you(out
of the microscope).

Realign the optics, making sure that you get the laser as close to the
end of the cantilever as possible and are getting as much light to the
photodiode as possible

Be sure that the laser is as close to the end of the cantilever as possible
and that you have a clear spot with your Align-o-Gadget.

Move the AFM to the isolation platform and use the Seuss hat.

Try another area of the sample or change samples, especially if you are
not seeing the kind of image you expected to see. Do not waste your time
with a bad sample.

Change tips, but don't throw away old tip. The tip might be salvageable.

4) Tip will not engage.

Make sure that something is not interfering with the tip reaching the sample
. This impediment may be as small as a big ridge on your sample

Check that you still have a cantilever . If you try to engage with
no cantilever the AFM will simply drive what's left of your tip into the
sample

5) Z Center Position reaches limit

This can happened when you move to a new region of the sample.
Go to the "Motor" menu and select "Step Motor" . Use the dialogue
box to seta value and move the tip up if you are at the retracted limit,
or tip down if you are at the extended limit. Usually ~ 200
nm will bring you back to a Z-Center Position of zero . Be careful
however. It can be very easy to hit the button too many times and
take your tip to the opposite limit.